BB's best card is a 7, marshall described why well.

Button best card is a K imo (a Ks may be better if you think the player is likely to c/r bluff fds). Since most players aren't slowplaying this board, you can form your range easily to give the opponent a beat down. If he's going to call the turn too much you can value bet really thinly and other hands with good equity will get to see a river, or if he's folding too much (which is more likely) you can just bluff everything, most will have some sort of equity.

A queen might be better if you think it's going to get more credit.